% m211oh79.tex (prev.: oh75.*) - Phyllotaxis
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\begin{center}\tcr{\rmH Phyllotaxis} \end{center} %\vspace{0pt}
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\begin{description}  

\item[\tcr{Phyllotaxis}] \tcg{(leaf arrangement):}

-- passage from one leaf (on a twig) to the next is given by a \tcr{screw
displacement} involving a rotation:
    
\end{description}
\exprow{1.1}
\noindent\begin{tabular}{lcl}
\tcr{Tree} & \tcr{Phyllotaxis} & \tcr{Description} \\
\tcg{Elm, basswood} & \mc{\scr\frac{1}{2}} & alternate on opp.\ sides \\
\tcg{Beech, hazel}  & \mc{\scr\frac{1}{3}} & rotation of \mc{\scr\frac{1}{3}} of a turn \\
\tcg{Oak, apricot}  & \mc{\scr\frac{2}{5}} & rotation of \mc{\scr\frac{2}{5}} of a turn  \\
\tcg{Poplar, pear}  & \mc{\scr\frac{3}{8}}& rotation of \mc{\scr\frac{3}{8}} of a turn  \\
\tcg{Willow, almond} & \mc{\scr\frac{5}{13}}& rotation of \mc{\scr\frac{5}{13}} of a turn  \\
etc.
\end{tabular}


\begin{description}
\item[\tcr{Observation:}] these fractions are quotients of \tcg{alternate} \tcr{Fibonacci numbers:} 
\mc{0,1,1,2,3,5,8,13,21,\ldots}

\item[\tcr{Other manifestations of phyllotaxis:}] \rule{0pt}{0pt}

-arrangement of \tcr{florets} on a \tcb{sunflower};

-arrangement of \tcr{scales} of a \tcb{fir cone};

-arrangement of the \tcr{helical whorls} on a \tcb{pineapple}: \mc{5} parallel rows sloping gently to the right, \mc{8} to the left, \mc{13} steeply to the right.
\end{description}
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